I have to choose the pairs below that satisfy (f o g)(x)=x
My hunch is pair 2, but I don't know if thats right... i guess there could be more than one pair.
pair 1
f(x) = x^2
g(x) = x^3
pair 2
f(x) = x+2
g(x) = x-2
pair 3
f(x) = 3x
g(x) = -2x
pair 4
f(x) = 2x
g(x) = x/2
2006-07-12 16:33:44 · 8 answers · asked by metsfan6986 1 in Science & Mathematics ➔ Mathematics
pairs 2 and 4 satisfy this condition.
pair 2: (x-2) +2 = x
pair 4: 2(x/2) = x
2006-07-12 16:38:53 · answer #1 · answered by prune 3 · 0⤊ 0⤋
pair 2 and 4
2006-07-13 00:08:58 · answer #2 · answered by reyna danaya 2 · 0⤊ 0⤋
pair 2 and 4
2006-07-12 23:38:07 · answer #3 · answered by ___ 4 · 0⤊ 0⤋
You must know this one:
(f o g)(x) = f[g(x)]
pair 1
(f o g)(x)
= f[g(x)]
= (x³)²
= x^6 â x
pair 2
(f o g)(x)
= f[g(x)]
= (x - 2) + 2
= x
pair 3
(f o g)(x)
= f[g(x)]
= 3(-2x)
= -6x â x
pair 4
(f o g)(x)
= f[g(x)]
= 2(x/2)
= x
Therefore, those pairs are pair 2 and 4.
^_^
2006-07-12 23:54:38 · answer #4 · answered by kevin! 5 · 0⤊ 0⤋
Pair 2 and 4 because (f o g)(x) is equal to f(g(x)) so in pair number 2:
f(x-2)= x-2+2 = x
And in pair number 4:
f(x/2) = 2x/2 = x.
2006-07-12 23:57:22 · answer #5 · answered by Tomomi 3 · 0⤊ 0⤋
pair 4
fog=2(x/2)=x
2006-07-12 23:36:59 · answer #6 · answered by raj 7 · 0⤊ 0⤋
let x = t for each pair find f(t) first then put this into g(x) if it simplifies to t then f and g are inverses
2006-07-12 23:47:11 · answer #7 · answered by ivblackward 5 · 0⤊ 0⤋
yup, 2 and 4 you have your inverses.
2006-07-12 23:50:11 · answer #8 · answered by raz 5 · 0⤊ 0⤋